/*
 * JEF - Copyright 2009-2010 Jiyi (mr.jiyi@gmail.com)
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package jef.concurrent.timer;

import java.lang.Thread.State;
import java.util.Date;

import jef.tools.ArrayUtils;

/**
 * A facility for threads to schedule tasks for future execution in a background
 * thread. Tasks may be scheduled for one-time execution, or for repeated
 * execution at regular intervals.
 * 
 * <p>
 * Corresponding to each <tt>Timer</tt> object is a single background thread
 * that is used to execute all of the timer's tasks, sequentially. Timer tasks
 * should complete quickly. If a timer task takes excessive time to complete, it
 * "hogs" the timer's task execution thread. This can, in turn, delay the
 * execution of subsequent tasks, which may "bunch up" and execute in rapid
 * succession when (and if) the offending task finally completes.
 * 
 * <p>
 * After the last live reference to a <tt>Timer</tt> object goes away <i>and</i>
 * all outstanding tasks have completed execution, the timer's task execution
 * thread terminates gracefully (and becomes subject to garbage collection).
 * However, this can take arbitrarily long to occur. By default, the task
 * execution thread does not run as a <i>daemon thread</i>, so it is capable of
 * keeping an application from terminating. If a caller wants to terminate a
 * timer's task execution thread rapidly, the caller should invoke the timer's
 * <tt>cancel</tt> method.
 * 
 * <p>
 * If the timer's task execution thread terminates unexpectedly, for example,
 * because its <tt>stop</tt> method is invoked, any further attempt to
 * schedule a task on the timer will result in an <tt>IllegalStateException</tt>,
 * as if the timer's <tt>cancel</tt> method had been invoked.
 * 
 * <p>
 * This class is thread-safe: multiple threads can share a single <tt>Timer</tt>
 * object without the need for external synchronization.
 * 
 * <p>
 * This class does <i>not</i> offer real-time guarantees: it schedules tasks
 * using the <tt>Object.wait(long)</tt> method.
 * 
 * <p>
 * Implementation note: This class scales to large numbers of concurrently
 * scheduled tasks (thousands should present no problem). Internally, it uses a
 * binary heap to represent its task queue, so the cost to schedule a task is
 * O(log n), where n is the number of concurrently scheduled tasks.
 * 
 * <p>
 * Implementation note: All constructors start a timer thread.
 * 
 * @author Josh Bloch
 * @version 1.19, 01/27/06
 * @see TimerTask
 * @see Object#wait(long)
 * @since 1.3
 */

public class Timer {
	/**
	 * The timer task queue. This data structure is shared with the timer
	 * thread. The timer produces tasks, via its various schedule calls, and the
	 * timer thread consumes, executing timer tasks as appropriate, and removing
	 * them from the queue when they're obsolete.
	 */
	private TaskQueue queue = new TaskQueue();

	/**
	 * The timer thread.
	 */
	private TimerThread thread = new TimerThread(queue);

	/**
	 * This object causes the timer's task execution thread to exit gracefully
	 * when there are no live references to the Timer object and no tasks in the
	 * timer queue. It is used in preference to a finalizer on Timer as such a
	 * finalizer would be susceptible to a subclass's finalizer forgetting to
	 * call it.
	 */
	@SuppressWarnings("unused")
	private Object threadReaper = new Object() {
		protected void finalize() throws Throwable {
			synchronized (queue) {
				thread.newTasksMayBeScheduled = false;
				queue.notify(); // In case queue is empty.
			}
		}
	};

	/**
	 * This ID is used to generate thread names. (It could be replaced by an
	 * AtomicInteger as soon as they become available.)
	 */
	private static int nextSerialNumber = 0;

	private static synchronized int serialNumber() {
		return nextSerialNumber++;
	}

	/**
	 * Creates a new timer. The associated thread does <i>not</i> run as a
	 * daemon.
	 * 
	 * @see Thread
	 * @see #cancel()
	 */
	public Timer() {
		this("Timer-" + serialNumber());
	}

	/**
	 * Creates a new timer whose associated thread may be specified to run as a
	 * daemon. A daemon thread is called for if the timer will be used to
	 * schedule repeating "maintenance activities", which must be performed as
	 * long as the application is running, but should not prolong the lifetime
	 * of the application.
	 * 
	 * @param isDaemon
	 *            true if the associated thread should run as a daemon.
	 * 
	 * @see Thread
	 * @see #cancel()
	 */
	public Timer(boolean isDaemon) {
		this("Timer-" + serialNumber(), isDaemon);
	}

	/**
	 * Creates a new timer whose associated thread has the specified name. The
	 * associated thread does <i>not</i> run as a daemon.
	 * 
	 * @param name
	 *            the name of the associated thread
	 * @throws NullPointerException
	 *             if name is null
	 * @see Thread#getName()
	 * @see Thread#isDaemon()
	 * @since 1.5
	 */
	public Timer(String name) {
		thread.setName(name);
	}
	
	/**
	 * 原java的Timer在构造时线程默认启动，这里改为线程默认不启动
	 * 调用start方法才启动
	 */
	public synchronized void start(){
		if(Thread.State.NEW==thread.getState())
			thread.start();
	}

	/**
	 * 返回计时器线程的状态
	 * @return
	 */
	public State getThreadState(){
		return thread.getState();
	}
	
	/**
	 * Creates a new timer whose associated thread has the specified name, and
	 * may be specified to run as a daemon.
	 * 
	 * @param name
	 *            the name of the associated thread
	 * @param isDaemon
	 *            true if the associated thread should run as a daemon
	 * @throws NullPointerException
	 *             if name is null
	 * @see Thread#getName()
	 * @see Thread#isDaemon()
	 * @since 1.5
	 */
	public Timer(String name, boolean isDaemon) {
		thread.setName(name);
		thread.setDaemon(isDaemon);
		thread.start();
	}

	/**
	 * Schedules the specified task for execution after the specified delay.
	 * 
	 * @param task
	 *            task to be scheduled.
	 * @param delay
	 *            delay in milliseconds before task is to be executed.
	 * @throws IllegalArgumentException
	 *             if <tt>delay</tt> is negative, or
	 *             <tt>delay + System.currentTimeMillis()</tt> is negative.
	 * @throws IllegalStateException
	 *             if task was already scheduled or cancelled, or timer was
	 *             cancelled.
	 */
	public void schedule(TimerTask task, long delay) {
		if (delay < 0)
			throw new IllegalArgumentException("Negative delay.");
		sched(task, System.currentTimeMillis() + delay, 0);
	}

	/**
	 * Schedules the specified task for execution at the specified time. If the
	 * time is in the past, the task is scheduled for immediate execution.
	 * 
	 * @param task
	 *            task to be scheduled.
	 * @param time
	 *            time at which task is to be executed.
	 * @throws IllegalArgumentException
	 *             if <tt>time.getTime()</tt> is negative.
	 * @throws IllegalStateException
	 *             if task was already scheduled or cancelled, timer was
	 *             cancelled, or timer thread terminated.
	 */
	public void schedule(TimerTask task, Date time) {
		sched(task, time.getTime(), 0);
	}

	/**
	 * Schedules the specified task for repeated <i>fixed-delay execution</i>,
	 * beginning after the specified delay. Subsequent executions take place at
	 * approximately regular intervals separated by the specified period.
	 * 
	 * <p>
	 * In fixed-delay execution, each execution is scheduled relative to the
	 * actual execution time of the previous execution. If an execution is
	 * delayed for any reason (such as garbage collection or other background
	 * activity), subsequent executions will be delayed as well. In the long
	 * run, the frequency of execution will generally be slightly lower than the
	 * reciprocal of the specified period (assuming the system clock underlying
	 * <tt>Object.wait(long)</tt> is accurate).
	 * 
	 * <p>
	 * Fixed-delay execution is appropriate for recurring activities that
	 * require "smoothness." In other words, it is appropriate for activities
	 * where it is more important to keep the frequency accurate in the short
	 * run than in the long run. This includes most animation tasks, such as
	 * blinking a cursor at regular intervals. It also includes tasks wherein
	 * regular activity is performed in response to human input, such as
	 * automatically repeating a character as long as a key is held down.
	 * 
	 * @param task
	 *            task to be scheduled.
	 * @param delay
	 *            delay in milliseconds before task is to be executed.
	 * @param period
	 *            time in milliseconds between successive task executions.
	 * @throws IllegalArgumentException
	 *             if <tt>delay</tt> is negative, or
	 *             <tt>delay + System.currentTimeMillis()</tt> is negative.
	 * @throws IllegalStateException
	 *             if task was already scheduled or cancelled, timer was
	 *             cancelled, or timer thread terminated.
	 */
	public void schedule(TimerTask task, long delay, long period) {
		if (delay < 0)
			throw new IllegalArgumentException("Negative delay.");
		if (period <= 0)
			throw new IllegalArgumentException("Non-positive period.");
		sched(task, System.currentTimeMillis() + delay, -period);
	}

	/**
	 * Schedules the specified task for repeated <i>fixed-delay execution</i>,
	 * beginning at the specified time. Subsequent executions take place at
	 * approximately regular intervals, separated by the specified period.
	 * 
	 * <p>
	 * In fixed-delay execution, each execution is scheduled relative to the
	 * actual execution time of the previous execution. If an execution is
	 * delayed for any reason (such as garbage collection or other background
	 * activity), subsequent executions will be delayed as well. In the long
	 * run, the frequency of execution will generally be slightly lower than the
	 * reciprocal of the specified period (assuming the system clock underlying
	 * <tt>Object.wait(long)</tt> is accurate).
	 * 
	 * <p>
	 * Fixed-delay execution is appropriate for recurring activities that
	 * require "smoothness." In other words, it is appropriate for activities
	 * where it is more important to keep the frequency accurate in the short
	 * run than in the long run. This includes most animation tasks, such as
	 * blinking a cursor at regular intervals. It also includes tasks wherein
	 * regular activity is performed in response to human input, such as
	 * automatically repeating a character as long as a key is held down.
	 * 
	 * @param task
	 *            task to be scheduled.
	 * @param firstTime
	 *            First time at which task is to be executed.
	 * @param period
	 *            time in milliseconds between successive task executions.
	 * @throws IllegalArgumentException
	 *             if <tt>time.getTime()</tt> is negative.
	 * @throws IllegalStateException
	 *             if task was already scheduled or cancelled, timer was
	 *             cancelled, or timer thread terminated.
	 */
	public void schedule(TimerTask task, Date firstTime, long period) {
		if (period <= 0)
			throw new IllegalArgumentException("Non-positive period.");
		sched(task, firstTime.getTime(), -period);
	}

	/**
	 * Schedules the specified task for repeated <i>fixed-rate execution</i>,
	 * beginning after the specified delay. Subsequent executions take place at
	 * approximately regular intervals, separated by the specified period.
	 * 
	 * <p>
	 * In fixed-rate execution, each execution is scheduled relative to the
	 * scheduled execution time of the initial execution. If an execution is
	 * delayed for any reason (such as garbage collection or other background
	 * activity), two or more executions will occur in rapid succession to
	 * "catch up." In the long run, the frequency of execution will be exactly
	 * the reciprocal of the specified period (assuming the system clock
	 * underlying <tt>Object.wait(long)</tt> is accurate).
	 * 
	 * <p>
	 * Fixed-rate execution is appropriate for recurring activities that are
	 * sensitive to <i>absolute</i> time, such as ringing a chime every hour on
	 * the hour, or running scheduled maintenance every day at a particular
	 * time. It is also appropriate for recurring activities where the total
	 * time to perform a fixed number of executions is important, such as a
	 * countdown timer that ticks once every second for ten seconds. Finally,
	 * fixed-rate execution is appropriate for scheduling multiple repeating
	 * timer tasks that must remain synchronized with respect to one another.
	 * 
	 * @param task
	 *            task to be scheduled.
	 * @param delay
	 *            delay in milliseconds before task is to be executed.
	 * @param period
	 *            time in milliseconds between successive task executions.
	 * @throws IllegalArgumentException
	 *             if <tt>delay</tt> is negative, or
	 *             <tt>delay + System.currentTimeMillis()</tt> is negative.
	 * @throws IllegalStateException
	 *             if task was already scheduled or cancelled, timer was
	 *             cancelled, or timer thread terminated.
	 */
	public void scheduleAtFixedRate(TimerTask task, long delay, long period) {
		if (delay < 0)
			throw new IllegalArgumentException("Negative delay.");
		if (period <= 0)
			throw new IllegalArgumentException("Non-positive period.");
		sched(task, System.currentTimeMillis() + delay, period);
	}

	/**
	 * Schedules the specified task for repeated <i>fixed-rate execution</i>,
	 * beginning at the specified time. Subsequent executions take place at
	 * approximately regular intervals, separated by the specified period.
	 * 
	 * <p>
	 * In fixed-rate execution, each execution is scheduled relative to the
	 * scheduled execution time of the initial execution. If an execution is
	 * delayed for any reason (such as garbage collection or other background
	 * activity), two or more executions will occur in rapid succession to
	 * "catch up." In the long run, the frequency of execution will be exactly
	 * the reciprocal of the specified period (assuming the system clock
	 * underlying <tt>Object.wait(long)</tt> is accurate).
	 * 
	 * <p>
	 * Fixed-rate execution is appropriate for recurring activities that are
	 * sensitive to <i>absolute</i> time, such as ringing a chime every hour on
	 * the hour, or running scheduled maintenance every day at a particular
	 * time. It is also appropriate for recurring activities where the total
	 * time to perform a fixed number of executions is important, such as a
	 * countdown timer that ticks once every second for ten seconds. Finally,
	 * fixed-rate execution is appropriate for scheduling multiple repeating
	 * timer tasks that must remain synchronized with respect to one another.
	 * 
	 * @param task
	 *            task to be scheduled.
	 * @param firstTime
	 *            First time at which task is to be executed.
	 * @param period
	 *            time in milliseconds between successive task executions.
	 * @throws IllegalArgumentException
	 *             if <tt>time.getTime()</tt> is negative.
	 * @throws IllegalStateException
	 *             if task was already scheduled or cancelled, timer was
	 *             cancelled, or timer thread terminated.
	 */
	public void scheduleAtFixedRate(TimerTask task, Date firstTime, long period) {
		if (period <= 0)
			throw new IllegalArgumentException("Non-positive period.");
		sched(task, firstTime.getTime(), period);
	}

	/**
	 * Schedule the specified timer task for execution at the specified time
	 * with the specified period, in milliseconds. If period is positive, the
	 * task is scheduled for repeated execution; if period is zero, the task is
	 * scheduled for one-time execution. Time is specified in Date.getTime()
	 * format. This method checks timer state, task state, and initial execution
	 * time, but not period.
	 * 
	 * @throws IllegalArgumentException
	 *             if <tt>time()</tt> is negative.
	 * @throws IllegalStateException
	 *             if task was already scheduled or cancelled, timer was
	 *             cancelled, or timer thread terminated.
	 */
	private void sched(TimerTask task, long time, long period) {
		if (time < 0)
			throw new IllegalArgumentException("Illegal execution time.");
		synchronized (queue) {
			if (!thread.newTasksMayBeScheduled)
				throw new IllegalStateException("Timer already cancelled.");

			synchronized (task.lock) {
				if (task.state == TimerTask.SCHEDULED)
					throw new IllegalStateException("Task already scheduled");
				task.nextExecutionTime = time;
				task.period = period;
				task.state = TimerTask.SCHEDULED;
			}

			queue.add(task);
			if (queue.getMin() == task)
				queue.notify();
		}
	}

	/**
	 * Terminates this timer, discarding any currently scheduled tasks. Does not
	 * interfere with a currently executing task (if it exists). Once a timer
	 * has been terminated, its execution thread terminates gracefully, and no
	 * more tasks may be scheduled on it.
	 * 
	 * <p>
	 * Note that calling this method from within the run method of a timer task
	 * that was invoked by this timer absolutely guarantees that the ongoing
	 * task execution is the last task execution that will ever be performed by
	 * this timer.
	 * 
	 * <p>
	 * This method may be called repeatedly; the second and subsequent calls
	 * have no effect.
	 */
	public void cancel() {
		synchronized (queue) {
			thread.newTasksMayBeScheduled = false;
			queue.clear();
			queue.notify(); // In case queue was already empty.
		}
	}

	
	public boolean isCancelled(){
		return !thread.newTasksMayBeScheduled;
	}
	
	/**
	 * Removes all cancelled tasks from this timer's task queue. <i>Calling this
	 * method has no effect on the behavior of the timer</i>, but eliminates
	 * the references to the cancelled tasks from the queue. If there are no
	 * external references to these tasks, they become eligible for garbage
	 * collection.
	 * 
	 * <p>
	 * Most programs will have no need to call this method. It is designed for
	 * use by the rare application that cancels a large number of tasks. Calling
	 * this method trades time for space: the runtime of the method may be
	 * proportional to n + c log n, where n is the number of tasks in the queue
	 * and c is the number of cancelled tasks.
	 * 
	 * <p>
	 * Note that it is permissible to call this method from within a a task
	 * scheduled on this timer.
	 * 
	 * @return the number of tasks removed from the queue.
	 * @since 1.5
	 */
	public int purge() {
		int result = 0;

		synchronized (queue) {
			for (int i = queue.size(); i > 0; i--) {
				if (queue.get(i).state == TimerTask.CANCELLED) {
					queue.quickRemove(i);
					result++;
				}
			}

			if (result != 0)
				queue.heapify();
		}

		return result;
	}
}

/**
 * This "helper class" implements the timer's task execution thread, which waits
 * for tasks on the timer queue, executions them when they fire, reschedules
 * repeating tasks, and removes cancelled tasks and spent non-repeating tasks
 * from the queue.
 */
class TimerThread extends Thread {
	/**
	 * This flag is set to false by the reaper to inform us that there are no
	 * more live references to our Timer object. Once this flag is true and
	 * there are no more tasks in our queue, there is no work left for us to do,
	 * so we terminate gracefully. Note that this field is protected by queue's
	 * monitor!
	 */
	boolean newTasksMayBeScheduled = true;

	/**
	 * Our Timer's queue. We store this reference in preference to a reference
	 * to the Timer so the reference graph remains acyclic. Otherwise, the Timer
	 * would never be garbage-collected and this thread would never go away.
	 */
	private TaskQueue queue;

	TimerThread(TaskQueue queue) {
		this.queue = queue;
	}

	public void run() {
		try {
			mainLoop();
		} finally {
			// Someone killed this Thread, behave as if Timer cancelled
			synchronized (queue) {
				newTasksMayBeScheduled = false;
				queue.clear(); // Eliminate obsolete references
			}
		}
	}

	/**
	 * The main timer loop. (See class comment.)
	 */
	private void mainLoop() {
		while (true) {
			try {
				TimerTask task;
				boolean taskFired;
				synchronized (queue) {
					// Wait for queue to become non-empty
					while (queue.isEmpty() && newTasksMayBeScheduled)
						queue.wait();
					if (queue.isEmpty())
						break; // Queue is empty and will forever remain; die

					// Queue nonempty; look at first evt and do the right thing
					long currentTime, executionTime;
					task = queue.getMin();
					synchronized (task.lock) {
						if (task.state == TimerTask.CANCELLED) {
							queue.removeMin();
							continue; // No action required, poll queue again
						}
						currentTime = System.currentTimeMillis();
						executionTime = task.nextExecutionTime;
						if (taskFired = (executionTime <= currentTime)) {
							if (task.period == 0) { // Non-repeating, remove
								queue.removeMin();
								task.state = TimerTask.EXECUTED;
							} else { // Repeating task, reschedule
								queue.rescheduleMin(task.period < 0 ? currentTime - task.period : executionTime + task.period);
							}
						}
					}
					if (!taskFired) // Task hasn't yet fired; wait
						queue.wait(executionTime - currentTime);
				}
				if (taskFired) // Task fired; run it, holding no locks
					task.run();
			} catch (InterruptedException e) {
			}
		}
	}
}

/**
 * This class represents a timer task queue: a priority queue of TimerTasks,
 * ordered on nextExecutionTime. Each Timer object has one of these, which it
 * shares with its TimerThread. Internally this class uses a heap, which offers
 * log(n) performance for the add, removeMin and rescheduleMin operations, and
 * constant time performance for the getMin operation.
 */
class TaskQueue {
	/**
	 * Priority queue represented as a balanced binary heap: the two children of
	 * queue[n] are queue[2*n] and queue[2*n+1]. The priority queue is ordered
	 * on the nextExecutionTime field: The TimerTask with the lowest
	 * nextExecutionTime is in queue[1] (assuming the queue is nonempty). For
	 * each node n in the heap, and each descendant of n, d, n.nextExecutionTime <=
	 * d.nextExecutionTime.
	 */
	private TimerTask[] queue = new TimerTask[128];

	/**
	 * The number of tasks in the priority queue. (The tasks are stored in
	 * queue[1] up to queue[size]).
	 */
	private int size = 0;

	/**
	 * Returns the number of tasks currently on the queue.
	 */
	int size() {
		return size;
	}

	/**
	 * Adds a new task to the priority queue.
	 */
	void add(TimerTask task) {
		// Grow backing store if necessary
		if (size + 1 == queue.length)
			queue = ArrayUtils.copyOf(queue, 2 * queue.length);

		queue[++size] = task;
		fixUp(size);
	}

	/**
	 * Return the "head task" of the priority queue. (The head task is an task
	 * with the lowest nextExecutionTime.)
	 */
	TimerTask getMin() {
		return queue[1];
	}

	/**
	 * Return the ith task in the priority queue, where i ranges from 1 (the
	 * head task, which is returned by getMin) to the number of tasks on the
	 * queue, inclusive.
	 */
	TimerTask get(int i) {
		return queue[i];
	}

	/**
	 * Remove the head task from the priority queue.
	 */
	void removeMin() {
		queue[1] = queue[size];
		queue[size--] = null; // Drop extra reference to prevent memory leak
		fixDown(1);
	}

	/**
	 * Removes the ith element from queue without regard for maintaining the
	 * heap invariant. Recall that queue is one-based, so 1 <= i <= size.
	 */
	void quickRemove(int i) {
		assert i <= size;

		queue[i] = queue[size];
		queue[size--] = null; // Drop extra ref to prevent memory leak
	}

	/**
	 * Sets the nextExecutionTime associated with the head task to the specified
	 * value, and adjusts priority queue accordingly.
	 */
	void rescheduleMin(long newTime) {
		queue[1].nextExecutionTime = newTime;
		fixDown(1);
	}

	/**
	 * Returns true if the priority queue contains no elements.
	 */
	boolean isEmpty() {
		return size == 0;
	}

	/**
	 * Removes all elements from the priority queue.
	 */
	void clear() {
		// Null out task references to prevent memory leak
		for (int i = 1; i <= size; i++)
			queue[i] = null;

		size = 0;
	}

	/**
	 * Establishes the heap invariant (described above) assuming the heap
	 * satisfies the invariant except possibly for the leaf-node indexed by k
	 * (which may have a nextExecutionTime less than its parent's).
	 * 
	 * This method functions by "promoting" queue[k] up the hierarchy (by
	 * swapping it with its parent) repeatedly until queue[k]'s
	 * nextExecutionTime is greater than or equal to that of its parent.
	 */
	private void fixUp(int k) {
		while (k > 1) {
			int j = k >> 1;
			if (queue[j].nextExecutionTime <= queue[k].nextExecutionTime)
				break;
			TimerTask tmp = queue[j];
			queue[j] = queue[k];
			queue[k] = tmp;
			k = j;
		}
	}

	/**
	 * Establishes the heap invariant (described above) in the subtree rooted at
	 * k, which is assumed to satisfy the heap invariant except possibly for
	 * node k itself (which may have a nextExecutionTime greater than its
	 * children's).
	 * 
	 * This method functions by "demoting" queue[k] down the hierarchy (by
	 * swapping it with its smaller child) repeatedly until queue[k]'s
	 * nextExecutionTime is less than or equal to those of its children.
	 */
	private void fixDown(int k) {
		int j;
		while ((j = k << 1) <= size && j > 0) {
			if (j < size && queue[j].nextExecutionTime > queue[j + 1].nextExecutionTime)
				j++; // j indexes smallest kid
			if (queue[k].nextExecutionTime <= queue[j].nextExecutionTime)
				break;
			TimerTask tmp = queue[j];
			queue[j] = queue[k];
			queue[k] = tmp;
			k = j;
		}
	}

	/**
	 * Establishes the heap invariant (described above) in the entire tree,
	 * assuming nothing about the order of the elements prior to the call.
	 */
	void heapify() {
		for (int i = size / 2; i >= 1; i--)
			fixDown(i);
	}
}
